Interference filter reflecting a certain wave length band within a given wave length range while letting pass other wave length bands of the range

ABSTRACT

The filter comprises a plurality of alternately high and low refracting light transmitting layers, applied on a light transmitting support, and reflecting a certain wave length band within a given wave length range while letting pass the other wave length bands of the range. The filter includes a periodically symmetrically constructed inner system between two reflection-reducing outer systems each constructed from a group of alternating high and low reflecting layers for the attenuation of undesired secondary reflection bands. The layers of one outer systm group have the same constant index of refraction nconst as a first layer group of the inner system. For any other layer of the outer system, having a variable index of refraction ni differing from nconst there is fulfilled the condition that the absolute value of the product nconst ni X d1 is less than this product for those inner system layers having an index of refraction differing from nconst and wherein d1 is the layer thickness. The constant index of refraction of one group of layers of an outer system may be equal to the index of refraction of the low refracting layers of the inner system or to the index of refraction of the high refracting layers of the inner system.

JJULUOI Unlted States Patent 1191 [111 3,759,604 Thelen 1 Sept. 18, 1973INTERFERENCE FILTER REF LECTING A Primary ExaminerDavid SchonbergCERTAIN WAVE LENGTH BAND WITHIN A Assistant Examiner-Ronald J. SternGIVEN WAVE LENGTH RANGE WHILE y McGleW e! LETTING PASS OTHER WAVE LENGTHBANDS OF THE RANGE A RA T [75] Inventor: Alfred Thelen, Triesen,Furstentum, The cPmpljises a plurality of alternately h andLiechtenstein low refractmg light transmittmg layers, applled on a lighttransmitting support, and reflecting a certain wave ASSISTICCI Bill"! fl l pr length band within a given wave length range while let- Balzels'Fmstemum- Llednenstem ting pass the other wave length bands of therange. The

[22] Filed: Sept 17, 1971 filter includes a periodically symmetricallyconstructed mner system between two reflect1on-reduc1ng outer PP 181,433systems each constructed from a group of alternating high and lowreflecting layers for the attenuation of un- [30] Foreign AppnummPriority desired secondary reflection bands. The layers of one Se t l 81970 Switzerland 1 3919/70 outer systm group have the same constantlndex of rep fraction a as a first layer group of the inner system.

For any other layer of the outer system, having a vari- 5 3|. able indexof refraction n differing from there 58 i [163466 is fulfilled thecondition that the absolute value of the product 11 n, Xd, is less thanthis product for those inner system layers having an index of refractiondiffer- References cued ing from n and wherein d is the layer thickness.

UNITED STATES PATENTS The constant index of refraction of one group oflayers 3,528,726 9/1970 Austin 350/166 of n o er ystem ay be equal tothe index of refraction of the low refracting layers of the inner systemor FORElGN PATENTS OR APPLICATIONS to the index of refraction of thehigh refracting layers 211,597 11/1957 Australia 350/166 of the inner y5 Claims, 12 Drawing Figures PATENTEDSEPI ems saw 02 or 10 wJ Q PATENTEDSEP1 8|973 SHEET 03 W10 Pmmm w 3.759.604

SHEET 0; HF 10 Ao/A FIG. 5

WU 05 HF 10 QUE JVQ

PATENTED SEP] 8 I973 'PATENTED SEP] 8 I973 SHEET 06 0F 10 N OE SBEET 080F 10 QUE SHEET 03 HF 10 FIELD OF THE INVENTION This invention relatesto so-called minus filters and, more particularly, to a novel andimproved minus filter providing for extensive smoothing of the ranges onboth sides of the blocking range.

BACKGROUND AND SUMMARY OF THE INVENTION The present invention relates toso-called minus filters, which are composed of a plurality ofalternately high and low refracting thin layers applied on a support. Bythe term minus filters, as used herein, there is to be understoodoptical filters which, within a given wave length range, reflect acertain wave length band but let pass radiation of other wave lengths.In the ideal case, therefore, the light transmission should be, startingfrom a wave length A toa wave length A,, 100 percent: from wave lengthA, to wave length A,, percent: and from wave length A, to wave length Aagain 100 percent. The wave length range from A, to A, is then calledthe operating range of the filter, the ranges from A, to Ag, and from A,to A the pass ranges, and the range from A, to A,, the blocking range.Such filters find multiple applications in optical technology. Forexample, they are important for measuring the dispersed light ofmonochromators. The basis for most multi-layer interference filterscomprises layer stacks built up periodically of high and low refractinglayers. For minus filters, there is usually used a layer sequenceaccording to the scheme A/2, B, A, B, B, A/2, where A is a layer withthe index of refraction n, and with a thickness of A, of the means wavelength A of the blocking range, A/2 is a similar layer but of half thethickness of A, namely A and B is a layer with the index of refractionn, and a thickness of A For the layer stack as a whole, there can bestated a so-called equivalent index of refraction N and an equivalentthickness 1 as a function of the wave length. For the equivalent indexof refraction, in accordance with the theory, there applies thefollowing equation:

For the equivalent thickness, there applies the following equation:

index of refraction becomes imaginary, as is the case in the vicinity ofA,,/ A= l, as shown in FIG. 2, the layer stack is highly reflecting andeach additional period, or layer pair, reduces the transmission in thereflection band further. It will be noted that the curves for the threedifferent refraction value ratios are similar, that is, the equivalentrefraction indices have similar dispersion characteristics. From thestructure of equation (1), it will be further noted that:

' Noun/n. ,,/N(2 an It is known that the transmission of a layerarrangement, of the kind described, on a support with the index ofrefraction u in a surrounding medium with the index of refraction n isthe same as for an arrangement with the same layer structure where allindices of refraction, including the indices of refraction of thesupport and of the surrounding medium, are replaced by their reciprocalvalues multiplied by a certain factor x. FIG. 3 schematicallyillustrates the construction of two such equivalent reciprocal systems.

In practice, the transmission ranges of ordinary multilayer interferencefilters never meet the stipulated requirements. Instead, due tosecondary reflection bands, the transmission curve always shows acertain waviness, and the elimination of such waviness is a main problemin the construction of interference filters. It has been found that thiswaviness is the more apparent the lower the transmission in the blockingrange is, that is, the greater the number of layers of which the filteris constructed. FIG. 2 illustrates the standardized transmission curveof -a A/4 multi-layer interference filter of 19 layers, where T is thetransmitted radiant energy and T the incident radiant energy, A the wavelength, and A the mean wave length of the blocking range. The index ofrefraction of the low refracting layers is 1.56, and that of the highrefracting layers is 2.34. Such a filter, which can be expressed, inabbreviated notation, by the expression 1.56/ H (LI-l) [1.56, with n2.34 and n,, 1.56, is not suitable for many applications in opticaltechnology because of its waviness.

Extensive elimination of this waviness, or so-called smoothing, seems tobe possible, according to the prior art, on only one side of theblocking range, but not simultaneously on both sides. It is known thatthe wavi ness in a given wave length range can be reduced if it ispossible correctly to match phase and reflection capacity for each wavelength of the operating range, by

means of two groups of auxiliary layers applied on both sides of thebasic system. This method, however, is very laborious, as a methodconsistently to be used for this solution of this problem was not known.While, in the maantime, it has been shown by several authors how filterscan be constructed which are well smoothed in a relatively wide wavelength range, again there is the restriction that, in a minus filter,only the transmission range on one side of the blocking range,selectively either the short wave or the long wave, could be smoothed.It has been found that an improvement on one side has resulted in aworsening on the other side.

In contradistinction, the objective of the present invention is toprovide a layer construction, for a minus filter, which permitsextensive smoothing on both sides of the blocking range.

The interference filter of the invention, comprising a plurality ofalternately high and low refracting lighttransmitting layers, applied ona light transmitting support, reflecting a certain wave length bandwithin a given wave length range while letting pass the radiation of theother wave lengths of this range, comprises a periodically symmetricallyconstructed inner system between two reflection-reducing outer systemscomposed of a group of high refracting and a group of low refractingalternating layers to attenuate undesired reflection bands. Inaccordance with the invention, the layers of one of the groups of outersystems have the same constant index of refraction n as a first layergroup of the inner system and, for any other layer with a variableindex. of refraction n, of the outer systems differing from n there isfulfilled the condition that the absolute value of the product m rid-Xd, is smaller than this product for the layers of the inner systemhaving an index of refraction differing from n with d, being the layerthickness. Such a filter can be realized in the following steps:

l. There is selected the two layer substances for the layers of theperiodic layer stack A/2, B, A, B, B, A/2, of the inner system.

2. There is determined the number v of the periods of the inner systemrequired to obtain the desired blocking range according to the followingequations:

ns .4 /"s"u)'( A/ s) s "L4 where T is the transmission at the referencewave length t in the center of the reflection band.

3. There is calculated the transition layers to be applied symmetricallyon opposite sides of the above layer stack, in such a way that, forradiation of the wave A these layers would have a reflection-freetransmission between the medium n,,, provided for the embedment of theentire layer arrangement, and the inner system, with the equivalentindex of refraction N.

The filter as thus calculated can be produced by known techniques, suchas preferably by vapor deposition of the layers under vacuum.Hereinafter, it will be shown how, in a development of the invention,the requirement of the embedment of the entire layer arrangement in amedium, equal on both sides and with the index of refraction 11 can becircumvented. It should be noted that the smoothing of the twotransmission ranges of a negative filter, in accordance with theinvention, is based on the fact that the strong dispersion of the indexof refraction N, which results for the periodic layer stack, isapproximately compensated by the similar dispersion of the two outersystems on both sides of the reflection band. As this compensation,however, can be complete only for a specific wave length pair, thecorrect selection of the reference wave lengths, in the calculation ofthe outer systems, is of great importance, and it is advisable tocalculate the outer systems for different wave lengths and to select thecase which is best for a certain application.

For an understanding of the principles of the invention, reference ismade to the following description of typical embodiments thereof asgraphically illustrated in the accompanying drawings:

BRIEF DESCRIPTION OF THE DRAWINGS In the drawings:

FIGS. 1, 2 and 3 are graphical representations of prior art interferencefilter constructions; and

FIGS. 4 through 12 are graphical representations of interference filterconstructions embodying the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS In the following description ofembodiments of invention, there is used the usual abbreviated notationfor the representation of layer structures. In this abbreviatednotation, the first number (if stated) is the index of refraction of themedium on one side of the layer system, 1.56 being, for example, a glasswith the index of refraction 1.56. The designations A, A1, A2, B, B1, B2etc. indicate different layers with the refractive values n n n n n n,etc. The thickness of these layers is established beforehand and, inconnection with the following description, there are always meant layersof M4 optical layer thickness, A being a reference wave length, and theoptical layer thickness being defined, as is known, by the product ofindex of refraction and geometric thickness.

Expressions such as A/2, B/2, 81/2, 82/2, etc. mean the respectivelayers but of half the optical layer thickness, that is, in the presentdescription, M8 instead of M4. A term in parenthesis, for example, (A/2,B/2, A/2) means a layer sequence with the respective layer, and a raisedindex or power indicates that the layer sequence stated in theparenthesis is repeated the respective number of times. It should benoted that, with such a repetition, layers of the same type may becontiguous, for example, two A/2 layers, which together, may be regardedas a single layer of the thickness A. Instead of (A/2, B', A/2), theremight therefore be written A/2 B A B A B A/2. For the representation ofsymmetrical layer structures with many layers, the first-named notationis often more practical. The number indicated last in an expressionmeans the index of refraction of the contiguous medium on the other sideof the layer system.

In the following, a first embodiment of the invention is described ingreater detail. There is taken, for the inner system, a symmetricallayer stack with six periods (v 6), with low refracting layers with theindex of refraction 11,, 1.56 and high refracting layers with the indexof refraction n, 2.34. That is, there is a stack of a total of 13 layerswith the construction A/2 B A B A B A B A B A B A/2, which may bewritten also as (A/2,B,A/2). According to the aforementioned formulae,this inner system has an equivalent index of refraction N and anequivalent total thickness v'r.

For the outer system providing a reflection-free transition between thisinner system and an embedding medium with the index of refraction m,there is selected, in this example, again a periodic layer system whichis equivalent to a reflection-reducing single layer. As is known, thereapplies for such a single-layer reflection reduction the followingequation:

the contiguous medium with N (n,,,n,,) the index of refraction of thereflection-reducing single layer, or here,

the equivalent index of refraction of the outer system equivalent tosuch a single layer. The thickness of a reflection-reducing single layerwould have to be M4, or an odd multiple thereof. This means that, forthe outer system, a corresponding equation must apply in the presentexample.

In order to obtain a good smoothing of the transmission curve,especially in the portions of the transmission range contiguous to theblocking range, which is of particular importance in many applications,there is selected, as the reference wave length M for the calculation ofthe outer systems, that wave length for which the periodic layer stackshows an equivalent thickness of 1- 3 \,,/8.

By insertion of I1 ='l.46, n, 2.34, and -r= 3 M8 in equation 2, there iscalculated MA 0.72, and, using equation 1, there is found, for thisratio, the equivalent index of refraction N (n n,) 1.95. From equations(6) and 1) there is then obtained, for n the value 1.91. As the bandwidth of a single layer reflection reduction is not very great, and thesmoothing is to be obtained especially in the vicinity of the reflectionband, the layer sequence A/2 B2 A/2 must be used twice. FIG. 4illustrates the transmission curve of the resulting overall arrangement.

According to the above statements, and in the usual abbreviatednotation, its construction is:

1.56 with n 1.56, n 2.34'and n 1.91.

Among the embodiments according to the invention, the layer constructionis particularly simple in those where either the index of refraction ofthe high refracting layers, or that of the low refracting layers, of theinner system, is equal to the index of refraction of the embedmentmedium. Especially advantageous solutions result when the outer systemsare so determined that the difference of the refraction value ofadjacent low-refracting and high-refracting layers gradually diminishesoutwardly within the outer system, starting from the constant value ofthis difference in the inner system, and reaches the smallest value withthe layers contiguous to the embedment medium.

FIGS. 5 and 6 illustrate two examples of this kind. The example of FIG.5 has the construction:

1.56 (A/2 B3 A/2) (A/2 B2 A/2) (A/2 Bl A/2) (A/2 B2 A/2) (A/2 B3 A/2)/1.56 with n, =1.56, 2.34, n 1.95, and n The example of FIG. 6 has thefollowing construction:

1.56 (A/2 B5 A/2) (A/2 B4 A/2) (A/2 B3 A/2) (A/2 B2 A/2) (A/2 B1A/2)(A/2 B2 A/2) (A/2 B3 A/2) (M2 B4 A/2) (A/2 B5 A/2)/ 1.56 with n1.56, n, 2.34, n 2.10, n 2.02, n 1.85, n. a l

In F IG. 5, only the long-wave side of the transmission curve (A,-,/A 1)is represented and, for comparison, there are entered, in addition, thecorresponding curves of the embodiments 4 and 6 Examples 6, 5 and 4illustrate, as can be seen from the construction scheme, four-stage,twostage, and single-stage outer systems for the transition from theinner system to the embedment medium, equal on both sides. andcorrespondingly also the waviness of the mentioned systems is different.

A four-stage outer system is also shown in the example of FIG. 7, andhas the following construction:

6 4.00 (M2 B5 A12) (A/2 B4 A/2) (A/2 B3 A/2) (M2 B2 A/2) (M2 B1 A/2)'(A/2 B2 A/2) (A/2 B3 A/2) (M2 B4 A/Z) (All B5 A/Z) 4.00 with n, 4.00, n1.80, n 1.99. n 2.35, n 2.96, "35 3.61.

It should be noted that this particular filter was embedded in ahigh-refracting medium having an index of refraction 4.

The invention can be applied also to inner systems which are notconstructed from M4 layers. FIG. 8 illustrates the equivalent index ofrefraction of a layer structure A-B-A for three different refractionvalue ratios. As can be seen, these curves are quite similar to those ofFIG. 1. Since, however, in this case, equation (3) is no longerapplicable, the reflection-reducing outer systems must be found by othermeans. A simple possibility is to use for the outer systems a structuresimilar to that of the inner systems (A-B-A), but with n, in the outersystem decreasing linearly from the interior outwardly. The following isan example of such a filter:

1.56 (A B5 A) (A B4 A) (A B3 A) (A B2 A) (A B1 A) (A B2 A) (A B3 A) (AB4 A) (A B5 A) /1.56 "A 1.56. n n 2.184, n n 1.872, and n 1.716.

FIG. 9 illustrates the transmission curve of this filter. Thelast-mentioned construction method can be applied to all refractionvalue ratios and also to periodic layer arrangements with more than twolayer materials.

The examples so far described require several layer substances. Inpractice, this entails a certain disadvantage, because layer materialswhich are satisfactory not only with regard to their optical propertiesbut also with regard to their vapor-depositional and mechanicalproperties are available in only a limited number. It is possible toreplace, in a layer system, layers of a given refraction value by layersof a different refraction value, but with changed thickness.

FIG. 10 illustrates the standardized equivalent index of refraction ofthe following layer structure:

aA/2 bB aA/2 with n /n,, const. 1.5 and C I (b-a)/(b+a) 0, 0.2, 0.4,0.6, 0.8, a and b being ratios whose absolute values are not fixed, withconstant refraction value ratio but different thickness ratio. For X /Aless than 1.6, these curves are comparable with those of FIGS. 1 and 8,leading to a layer system with the structure 1/56/ (a A/2 b B a A/2) (a,A/2 b, B a, A/2) (a A/2 b B a A/2) (a A/2 b B 4 A/2) /1.56 with n,, 1.56and n, 2.34 and a, a 1.0 and b 0.10, b,=0.20, b 1.00. The transmissioncurve of this particular example is illustrated in FIG. 11. Thedisadvantage of this solution, which requires only two different layersof material, is, however, that a larger number of transition layers isneeded.

In the above examples, the point of departure was that the layer systemis embedded in a medium which is equal on both sides, whose index ofrefraction coincides with the index of refraction of either thehighrefracting or the low-refracting layers of the inner system. Thiscondition, which cannot always be met in practice, can be circumventedby inserting additional reflection-reducing layers between the mentionedouter systems and the adjacent media, and not fulfilling the mentionedcondition. The calculation of these additional reflection-reducinglayers, which must be determined so that a reflection-free transitionbetween the outer systems and the adjacent media, of any desired indexof refraction, is obtained, is effected in a known manner analogously tothe above-described method for the determination of thereflection-reducing outer systems.

FIG. 12 illustrates the transmission curve of a minus green filter,based on a construction similar to that of FIG. 4 but where the adjacentmedia are constituted by glass, as the support, and air. The exampleillustrated in FIG. 12 has the following structure:

1.52 (3B2 3A) (3Bl 3A) (382 3.4)82 B2 B3 71,4 n 2.34, n "B3 1.38, and t530nm In all the examples, the structure of the filter is stated, andthe structure is defined by the thicknesses and refraction indices ofthe layers. The invention relates only to this structure, and not to thequestion of how an individual layer of a certain thickness and a certainindex of refraction is produced. For the refraction indices mentioned inthe examples, the specialist in the art has corresponding layermaterials at his disposal. As mentioned above, vapor deposition undervacuum presently consitutes the most common method for the applicationof the layers on corresponding supports, usually glass plates. However,the layer structures according to the invention can be realizednaturally also with other layer production methods, for example, bycathode sputtering of the layer materials or by chemical depositions.With respect to the technology of layer production, there is anextensive trade literature. As an example, there may be mentionedHandbook of Thin Film Technology by Leon 1. Maissel and Reinhard Glang,published by McGraw-Hill Book Company in 1970.

While specific embodiments of the invention have been shown anddescribed in detail to illustrate the application of the principles ofthe invention, it will be understood that the invention may be embodiedotherwise without departing from such principles.

What is claimed is:

1. In an interference filter comprising a plurality of alternately highand low refracting light transmitting layers, applied on a lighttransmitting surface, reflecting a certain wave length band within agiven wave length range while letting pass other wave length bands ofthe range, which filter includes a periodically symmetricallyconstructed inner system between two reflection-reducing outer systemseach constructed from alternating high and low refracting layers, whereall low refracting layers form one group of the outer systems and allhigh refracting layers form another group of the outer systems, andwherein all low refracting layers of said inner system form a firstgroup and all high refracting layers of said inner system form a secondgroup, for the attenuation of undesired secondary reflection bands: theimprovement comprising the layers of one outer system group having thesame index of refraction n as one layer group of said inner system andeach other layer of the outer systems having an index of refraction mdifl'ering from n and fulfilling the condition that the absolute valueof the product m m I X d, is less than this product for the other group.of inner system layers having an index of refraction differing fromwhere d is the layer thickness.

2. In an interference filter, the improvement claimed in claim 1, inwhich the index of refraction of one group of layers of the outer sytemsis equal to the index of refraction of the low-refracting layers of theinner system.

3. In an interference filter, the improvement claimed in claim 1, inwhich the index of refraction of one group of layers of the outersystems is equal to the index of refraction of the high-refractinglayers of the inner system.

4. In an interference filter, the improvement claimed in claim 1, inwhich the outer systems have the layer sequence A/2, B1, A, B1, A/2,where A is a layer of M4 optical thickness and B1 is a layer with adifferent index of refraction but also having )t/4 optical thickness, Arepresenting the wave length of minimum transmission of the filter.

5. In an interference filter, the improvement claimed in claim 1, inwhich the absolute value of the product ri n, d,, for the additionallayers of the outer system differing in their index of refraction from nof one group of layers thereof, decreases from the interior outwardly.=0 l

1. In an interference filter comprising a plurality of alternately highand low refracting light transmitting layers, applied on a lighttransmitting surface, reflecting a certain wave length band within agiven wave length range while letting pass other wave length bands ofthe range, which filter includes a periodically symmetricallyconstructed inner system between two reflection-reducing outer systemseach constructed from alternating high and low refracting layers, whereall low refracting layers form one group of the outer systems and allhigh refracting layers form another group of the outer systems, andwherein all low refracting layers of said inner system form a firstgroup and all high refracting layers of said inner system form a secondgroup, for the attenuation of undesired secondary reflection bands: theimprovement comprising the layers of one outer system group having thesame index of refraction nconst as one layer group of said inner systemand each other layer of the outer systems having an index of refractionni differing from nconst, and fulfilling the condition that the absolutevalue of the product nconst - ni X di is less than this product for theother group of inner system layers having an index of refractiondiffering from nconst, where di is the layer thickness.
 2. In aninterference filter, the improvement claimed in claim 1, in which theindex of refraction of one group of layers of the outer sytems is equalto the index of refraction of the low-refracting layers of the innersystem.
 3. In an interference filter, the improvement claimed in claim1, in which the index of refraction of one group of layers of the outersystems is equal to the index of refraction of the high-refractinglayers of the inner system.
 4. In an interference filter, theimprovement claimed in claim 1, in which the outer systems have thelayer sequence A/2, B1, A, B1, A/2, where A is a layer of lambda /4optical thickness and B1 is a layer with a different index of refractionbut also having lambda /4 optical thickness, lambda representing thewave length of minimum transmission of the filter.
 5. In an interferencefilter, the improvement claimed in claim 1, in which the absolute valueof the product nconst - ni di, for the additional layers of the outersystem differing in their index of refraction from nconst of one groupof layers thereof, decreases from the interior outwardly.